Physics Formalism Helmholtz Matrix to Coulomb Gage

Abstract

Iyer Markoulakis Helmholtz Hamiltonian mechanics formalisms mathematically modeled physics with vortex rotational fields acting with gradient fields, typically in zero-point microblackhole general fields. Here, Helmholtz metrics have been gaged to Coulombic Hilbert metrics, representing Gilbertian and Amperian natures of electromagnetic fields out of the mechanical fields from Helmholtz Hamiltonian mechanics. This ansatz general gaging helps to properly isolate field effects – mechanical, electric, magnetic components within the analytical processes. Vacuum gravitational fields and the flavor Higgs-Boson matter inertial gravitational fields have been thus quantified extending to stringmetrics constructs matrix showing charge asymmetry gage metrics, having the power to analyze dark energy superluminal phase, dark matter luminal phase, and light matter subluminal phase. Interpreting particle physics gage matrix pointing to Dirac seas electrons, monopoles with positrons, electron-positron annihilation leading to energy production, relativistic energy generating matter, and both monopoles – vacuum and compressed out of vortex Helmholtz decomposition fields have been interpolated. Quantum ASTROPHYSICS gage metrix posits superluminal profile of signals velocity generating electron-positron chain like “curdling” action that is consistent with physics literature reporting nature electron photon observed oscillatory fields configurations. This helps proposing creation of neutrino antineutrino pair orthogonal to electron positron “curdling” planes, that may lead to formation of protonic hydrogen of stars or orthogonally muon. These aspects will explain receding or fast expanding universe with dark matter in terms of flavor metrics versus gage associating metrics flavor. Additional interpretations of virtual gravitational dipoles that have gravitational charge of opposite signs, reported per physics literature at Planck dimensions, that may originate at the center of supermassive blackhole. On the other hands, vacuum monopoles occur probably at infinity with cosmos extent.

Helmholtz Hamiltonian Mechanics Electromagnetic Physics Gaging Generalizing Mass-Charge and Charge-Fields Gage Metrics to Quantum Relativity Gage Metrics

“…Here, [ PDPcg ] matrix Equation ( 8) is like SUSY [12], having Hermitian quantum matrix [13,14]. With electron-positron annihilation alongside monopoles north and south collapsing to dipolar "stable" magnetism, that is like stringmetrics gage [5]; however, in this case it will be like electromagnetic gaging fields [6][7][8][9][10].…”

“…Time fields that are typical of microblackholes, shown to be analytically evidenceable from differential equations will determine these processes [4]. Iyer Markoulakis Helmholtz Hamiltonian general formalisms have been aptly converted to gage matrix [5], following physics literature procedures. Transformation of Helmholtz metrics to Coulomb gage, linking also Coulomb branch gage group with Hilbert series has also been quantifiably achieved having gradient fields converted to Coulomb gage, with rotational vortex fields branching to Hilbert gauge mass metrics of Higgs-Boson matter, and conforming to partial differential equations of vortex and the gradient fields obtained per Iyer Markoulakis original general formalism [1,5].…”

“…Iyer Markoulakis Helmholtz Hamiltonian general formalisms have been aptly converted to gage matrix [5], following physics literature procedures. Transformation of Helmholtz metrics to Coulomb gage, linking also Coulomb branch gage group with Hilbert series has also been quantifiably achieved having gradient fields converted to Coulomb gage, with rotational vortex fields branching to Hilbert gauge mass metrics of Higgs-Boson matter, and conforming to partial differential equations of vortex and the gradient fields obtained per Iyer Markoulakis original general formalism [1,5]. Vacuum gravitational solutions of the fields provided means to arrive at unitary determinant that will analytically project to having almost infinite extension of gauge matrix metrics, like stringmetrics construct showing typically charge asymmetry gage metrics [5].…”

“…Transformation of Helmholtz metrics to Coulomb gage, linking also Coulomb branch gage group with Hilbert series has also been quantifiably achieved having gradient fields converted to Coulomb gage, with rotational vortex fields branching to Hilbert gauge mass metrics of Higgs-Boson matter, and conforming to partial differential equations of vortex and the gradient fields obtained per Iyer Markoulakis original general formalism [1,5]. Vacuum gravitational solutions of the fields provided means to arrive at unitary determinant that will analytically project to having almost infinite extension of gauge matrix metrics, like stringmetrics construct showing typically charge asymmetry gage metrics [5]. Results of general formalism have been also discussed extensively with Physical analysis of particle physics gage matrix pointing to Dirac seas of electrons, monopoles with positrons, electron-positron annihilation leading to energy production, and the relativistic energy generating matter; quantum astrophysics gage metrix proposed mechanism of creation of neutrino antineutrino pair orthogonal to electron positron "curdling" planes, that may lead to the formation of protonic hydrogen of stars or orthogonally to these "curdling" planes muon particles, that are consistent with physics literature, have been elaborated further with concept of the vacuum monopoles posed to occur at extent of infinite cosmos [1,3,5].…”

“…Section 2.1 configures application modeling using rules of Iyer Markoulakis Helmholtz Hamiltonian mechanics to evaluate eigenvector field bundle matrix of Pauli Dirac dipole biased monopoles+ electron-positron particle gaged field circuit, evaluating string gage metrics. Section 3 proceeds Physical Analysis with Results and Discussions, having Section 3.1 discussing by a brief note knowhow of generalizing mass-charge quantum metrics from general formalism of Iyer Markoulakis [1] and that of charge-fields obtained per Section 2 using proof formalism [4] and physics formalism [5] to define observable measurable gage metrics. Section 3.2 encompasses general relativistic time space sense symmetry shaping aspects with pressure matter gage metrics, as well as electro-magnetic gage metrics fields via quantum Helmholtz Hamiltonian mechanics formalized originally with theory of Iyer Markoulakis generalization provided [1], evaluating Coulomb gage out of fundamental proof formalism [4] in terms of pure state's coupling constant quantum density matrix with a function operator quantifying action vortex wavefunctions and the scalar potential of gradient up energy.…”